4 ms·
They grow very quickly. The median third and fourth primes are 42719 and 5737850066077 - see https://oeis.org/A284411 https://oeis.org/A284411 . If p_k^* is t
by madcaptenor 3y ago
They grow very quickly. The median third and fourth primes are 42719 and 5737850066077 - see https://oeis.org/A284411 https://oeis.org/A284411 .
If p_k^* is the median kth prime then we have
log log p_k^* = k - C + O(1/sqrt(k))
where C is a constant around 0.59483; that is, p_k^* grows like exp(exp(k)). This is "Corollaire 1.2" of the paper that the post links to (https://tenenb.perso.math.cnrs.fr/PPP/p_k%28n%29.pdf https://tenenb.perso.math.cnrs.fr/PPP/p_k%28n%29.pdf). (It's in French.)